This paper describes a prototype and analytical studies of a spherical rolling robot, a new design of an omnidirectional robot system. The robot can arbitrarily begin to move in any direction to the target, and autonomously roll and reach any desired position. Our design considers a spherical robot with an internal mechanism for propulsion. The propulsion mechanism distributes weights radially along spokes fixed inside the sphere and enables the robot to accelerate, decelerate, and move with constant velocity. A mathematical model of the robot's dynamic and motion is instructed. An algorithmic motion planning is developed and, partly, pseudo-code of that is presented. For a number of missions, it is shown experimentally that the model agrees well with the results.